Highlights The generalized logistic equation is used to interpret the COVID-19 epidemic data. The model describes properly the growth in the number of confirmed cases with time. The actual data and logistic curves are shown. The logistic model can describe the number of sick people per day.

The paper reports on application of the Gompertz model to describe the growth dynamics of COVID-19 cases during the first wave of the pandemic in different countries. Modeling has been performed for 23 countries: Australia, Austria, Belgium, Brazil, Great Britain, Germany, Denmark, Ireland, Spain, Italy, Canada, China, the Netherlands, Norway, Serbia, Turkey, France, Czech Republic, Switzerland, South Korea, USA, Mexico, and Japan. The model parameters are determined by regression analysis based on official World Health Organization data available for these countries. The comparison of the predictions given by the Gompertz model and the simple logistic model (i.e., Verhulst model) is performed allowing to conclude on the higher accuracy of the Gompertz model.

In the present study we consider propagation of a localized internal perturbation in the form of an oscillating wave packet (breather) of the first mode in a three-layer fluid with an uneven bottom shaped as a smoothed step. The study is carried out by methods of numerical simulation within a fully nonlinear two-dimensional (vertical plane) set of NavierStokes equations. A set of calculations was carried out for different widths and heights of the bottom step. Inhomogeneity of the medium leads to transformation of the internal wave field with the formation of weak reflected waves and one or two first-mode breathers passed to the shallow zone. By analyzing linear stability in terms of Richardson and Froude numbers, it was revealed that potentially unstable regions arise at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves was performed. The vertical mode composition of the fully nonlinear wave field is analyzed. It is shown that the first mode makes the largest contribution to the vertical structure of the full-nonlinear packet, though the fourth, second and the third modes also contribute noticeably.